While these are the correct words (though I believe "quaereo" should be "quaero"), it's no good grammatically.

veritas semper petendus

This would work if it were "petenda" (from the verb "peto" to seek). But if you really must have the imperative mood, this is not it. As is, this means "truth always (is) to be sought".

As others have put, the best sentence is probably something like "pete semper veritatem" or "quaere semper veritatem". You could possibly use "veritati" in either of those expressions, meaning "seek to the truth", a bit odd in English, but not so much in Latin.

the phrase definitely necessitates a gerundive here, however the brevity of the phrase makes the use of any adverb ugly and nigh on superfluous.
as opposed to using the verb "peto" which contains a different sense of seeking (viz. physically striving towards something), it would be better, it seems to me, to use a form based upon "quaero", as wisely suggested.
so as to highlight the frequentative nature of the seeking of truth (on this, the mental level of seeking something out ), why not use just that - the frequentative form of this verb, i.e. "quaerito" (1)? with this particular, yet oft-neglected, verb, the sense of the constant necessity to seek truth is captured without the need of an adverb.

thus "veritas quaeritanda"

what is better, all the more, is that this little phrase is itself a clausula, so beloved of Classical prose writers.
The first three syllables are the common Cretic and are followed by two Trochees. This cretic-trochee-trochee/spondee tends to be the third favourite of various prose clausulae and is evident in such phrases as: